Vaccination dilemma with imperfect vaccination efficiency

Abstract

Achieving widespread population immunity by voluntary vaccination poses a major challenge for public health
administration and practice. The situation is complicated even more by imperfect vaccines. How the vaccine efficacy affects
individuals vaccination behavior has yet to be fully answered. To address this issue, we combine a simple yet effective game
theoretic model of vaccination behavior with an epidemiological process. Our analysis shows that, in a population of selfinterested
individuals, there exists an overshooting of vaccine uptake levels as the effectiveness of vaccination increases.
Moreover, when the basic reproductive number, R0, exceeds a certain threshold, all individuals opt for vaccination for an
intermediate region of vaccine efficacy. We further show that increasing effectiveness of vaccination always increases the
number of effectively vaccinated individuals and therefore attenuates the epidemic strain. The results suggest that number
is traded for efficiency: although increases in vaccination effectiveness lead to uptake drops due to free-riding effects, the
impact of the epidemic can be better mitigated.